Bubble Response Research Articles

Numerical simulation of scattering of TWIPS by underwater air bubble

Abstract The interaction of water with the subsurface of sea-ice leads to the generation of air bubbles. This heterogeneity results in additional challenges for unmanned underwater vehicles (UUV) conducting active detection in the upper water column of the Arctic Ocean. Under excitation by a high-amplitude acoustic source, asymmetric oscillations of the bubble are generated due to the high compressibility of gas, which further leads to acoustic scattering showing nonlinear characteristics. The corresponding signals may interfere with or even mask the echoes from potential targets, which are often linear scatterers, ultimately impairing the UUV’s active sensing capabilities under the sea-ice. Twin Inverted Pulse Sonar (TWIPS) is an underwater detection technique consisting of sending two pulse signals of equal amplitude but with opposing phases, benefiting from the difference in the responses of the bubble and target and the resulting echo signals for the eventual distinguishing. In this study, a numerical modeling of underwater bubbles for the acoustic study is developed by making use of both multiphysics and moving mesh features of Comsol. Numerical simulations were conducted to investigate the nonlinear feature of acoustic scattering from air bubbles. These results are then compared with analytical results for verification. Monochromatic signals and TWIPS at different frequencies are used as excitation signals, and the response of spherical air bubbles and the resulting scattered wave field are calculated, compared, and analyzed.

Nonlinear Vibrations of the Piezoelectric-Laminated Composite Cantilever Rectangular Plate Subjected to the Transverse and Parametric Excitation

The intelligent structure will be the key to the industrial manufacturing field in the future, piezoelectric materials are the most commonly used active materials in many mechatronic and vibration control systems. In this paper, we illustrated the nonlinear vibration behaviors of the piezoelectric-laminated composite cantilever rectangular plate subjected to transverse and parametric excitation. Two piezoelectric layers are attached to the upper and lower surfaces of graphite/epoxy composite laminated plate. The nonlinear dynamic equations are derived via the classical laminated plate theory, von Karman large deformation theory, the constitutive equation of the piezoelectric materials, and the Hamilton principle. Considering the Galerkin method, the nonlinear ordinary differential equations for the two-order vibration mode of the piezoelectric laminated composite cantilever rectangular plate are achieved. The multiple scale method is applied to obtain the average equations to study the nonlinear vibration characteristic of the stable motion. The primary resonance and the 1:1 internal resonance of the piezoelectric laminated composite cantilever rectangular plate are investigated. The amplitude-frequency response curves, force-amplitude response curves, time histories, phase curves, and bifurcation diagrams are given to investigate the nonlinear dynamic characteristic of the piezoelectric laminated composite cantilever rectangular plate. The detailed parametric analyses show that bubble response curves are separated from the amplitude-frequency response curves with the continuous increase of the external excitation due to the internal resonance. In addition, the results reveal the energy transform between the various order vibration modes of the system. This work is expected to provide theoretical guidance for the nonlinear vibration of the smart piezoelectric laminated composite structure.

The comovement of bubbles’ responses to monetary policy shocks

In this paper, we present a two-step methodology designed to elucidate the extent of co-movement in the behavior of asset bubbles across a selected group of developed and emerging economies, with observations extending from the year 2000 onwards. We characterize the behavior of these bubbles, conceptualized as the disparity between fundamental and market values, by examining their responses to monetary policy shocks. Our investigation into their co-movement dynamics post-2000 involves the estimation of a Bayesian Dynamic Factor Model that incorporates the reactions of asset bubbles to monetary policy shocks, both in the short term and the long term. Notably, our findings reveal a convergence in short-term responses among these bubbles prior to the onset of the financial crisis. However, as the crisis unfolded, our results indicate a shift towards divergence. Concerning the long-term response of bubbles to monetary policy, divergence was observed before the crisis, but once the crisis had taken hold, there was a noticeable trend towards convergence. An influential idiosyncratic factor was identified for countries like the United States, South Korea, and Japan, impacting both short-term and long-term behavior. Conversely, the long-term behavior of bubbles in most emerging economies appears to be influenced by idiosyncratic factors. Furthermore, our results largely maintain their robustness even when utilizing an alternative measure of monetary policy stance during the period of the zero lower bound. Nevertheless, this secondary analysis suggests heightened volatility in the factors affecting both emerging and advanced markets.

Dynamic response of He bubbles in Fe9Cr1.5W0.4Si F/M steel under in-situ stepwise nanocompression

Inert-gas bubbles in metals have attracted great attention due to their fundamental role in swelling and degradation of materials. Studies of bubble behavior can provide valuable insights for developing advanced materials. Although extensive research has been conducted on bubble behavior under irradiation or thermal conditions, there is still a lack of investigation under both stress and temperature conditions. In this work, in-situ uniaxial compression tests were performed on helium-bubbled Fe9Cr1.5W0.4Si F/M steel using transmission electron microscopy at 923 K to investigate the responses of bubbles with increasing strain. The results revealed a series of bubble responses, including frequent annihilation, occasional coalescence, and a "forced" coalescence achieved by connecting multiple bubbles under high strain. These responses relied on bubble migration and interaction, influenced by the factors such as the He-V ratio, relative bubble position, and sink effect. Furthermore, the migration mechanism of compressed bubbles at high temperatures is considered to be a combination of surface diffusion induced by thermal gradient and volume diffusion induced by stress gradient. These two mechanisms are expected to compete with each other in different temperature and stress. These findings offer crucial experimental insights into the behavior of bubbles in solids exposed to stress and thermal conditions.

Destabilizing surface bubbles with excessive bulk oversaturation

The response and dynamics of surface-attached bubbles in gas-oversaturated environments have practical implications for industrial processes such as photocatalytic water splitting. Surprisingly, the behavior of microbubbles and nanobubbles depends rather strongly on the nucleation techniques, e.g., solvent exchange gives rise to stable bubbles, while other methods like electrochemical water splitting produce unstable ones. By experimentally investigating a prototypical system of bubble nucleation, we show how these outcomes are determined by a competition between gas oversaturation and contact line friction. We derive a stability line in the oversaturation-radius parameter space, which not only agrees with our experiments but also correctly predicts the outcome of previous experiments across five orders in oversaturation and bubble radius.

Controlling the stability of monodisperse lipid-coated microbubbles by tuning their buckling pressure

Through recent years, major hurdles associated with the microfluidic production of phospholipid-coated monodisperse microbubble have been overcome which has granted them a long shelf life. This has heaved the hope of using their unique properties in vivo for improved contrast, controlled therapy, or noninvasive pressure measurement. However, these bubbles are also very sensitive to small changes in ambient pressure which compromises their clinical translation: upon intravenous injection, physiological pressures will cause bubble dissolution, degrading their uniformity. Here, we demonstrate the direct relation between shell buckling and bubble dissolution by acoustically measuring the buckling pressure and the response of bubbles to controlled pressure changes. We show that the concentration of PEGylated lipid, necessary for microfluidic operation, can be used to tune the buckling pressure, and thereby increase bubble stability. We show that this concentration can be changed either directly during bubble production or, more conveniently, by heating the microbubbles after production. The proposed heating step exploits the phase-change of the phospholipids within the shell to selectively expel the PEGylated lipids. Doing so, the bubble buckling pressure can be increased from 0 kPa to 27 kPa which is above physiological pressures.

Focused ultrasound pulse repetition frequency impacts bubble activity and tracer delivery during blood-brain barrier opening

The impact of pulse repetition frequency (PRF) on microbubble activity and blood-brain barrier (BBB) opening, for a fixed total number of pulses, is unclear. We studied bubble response to a range of PRFs (0.125, 0.25, 0.5, 1, and 2 Hz) by monitoring bubble emissions during focused ultrasound (FUS) sonications of the rat brain (274.3 kHz). When a location was treated with a test PRF and a control PRF of 1 Hz, at the same pressure, the change in the harmonic amplitude compared to the control decreased with increasing PRF, with a median change of 73.8% at 0.125 Hz and −38.3% at 2 Hz. Significant changes were not observed with repeated sonications at the same PRF. Furthermore, between PRFs of 0.25 and 1 Hz, no difference was observed in the threshold for broadband emissions, which are linked to the potential for tissue damage. Fluorescence imaging was used to estimate the concentration of Trypan Blue (TB) dye following a fixed-pressure 75-pulse exposure for PRFs of 1 and 0.25 Hz in rats. A 0.25 Hz PRF led to a 68.2% increase in the mean concentration measured at the target, with a 53.9% increase in the mean harmonic sum compared with a 1 Hz PRF. Finally, a harmonic emissions-based controller at a PRF of 0.25 Hz yielded similar TB delivery, with fewer instances of petechiae observed through histology, compared to the same controller at 1 Hz. These results may be adapted to improve the clinical safety margin of FUS-mediated BBB opening and to improve the sensitivity to detecting small harmonic signals from cavitating microbubbles.

A data-driven analysis of short and long laminar separation bubbles

This work investigates the statistical response of short and long laminar separation bubbles to external flow parameters, such as Reynolds number, free-stream turbulence intensity and streamwise pressure gradient, known to govern bubble formation and characteristics. A parametric experimental campaign has been performed using particle image velocimetry on a flat plate to provide a comprehensive database for the characterization of separation-induced transition in both short and long separation bubbles. The proper orthogonal decomposition (POD) was applied to the data set of all dividing streamlines commonly used to identify a laminar separation bubble. This provides an optimal state-space basis for the data-driven classification of the state of a laminar separation bubble, with the leading modes capturing the change in length and height of the laminar separation bubble in response to changes in the flow parameters. When projected onto the POD subspace constituted by the first three leading modes, the normalized data from the present study and the results from prior investigations not used in the modal analysis collapse on the same trajectory in the low-dimensional space. The present POD basis can be therefore adopted for the description of the general response of the time-mean shape of a laminar separation bubble to changes in the main influencing parameters. A well-defined pattern was observed in the case of short laminar separation bubbles in the reduced-order space defined by the first three POD coefficients, whereas a higher dispersion in the long-bubble regime indicates an increased sensitivity of long bubbles to the external flow characteristics.

Shrinkage and coalescence behavior of helium bubbles in Fe9Cr1.5W0.4Si F/M steel under the coupling effect of compression stress and temperature

As important irradiation defects, helium bubbles will threaten the stability and reliability of reactor structural materials. Extensive research has been conducted on the dynamic response of helium bubbles under thermal annealing, irradiation, or tension, but the behavior and mechanisms of helium bubble evolution under compression remain to be understood. Here, by adopting in-situ cyclic nanocompression testing on Fe9Cr1.5W0.4Si F/M steel containing helium bubbles at 673 K, we present direct experimental evidence for the shrinkage and coalescence behavior of helium bubbles under the coupling effect of compression stress and temperature for the first time. Unlike the stress-free condition where the bubble size shows an increasing trend, compressive stress causes the bubble to shrink. Moreover, the large-sized bubbles show a greater change in size than small-sized bubbles. At 673 K, there is no thermal motion of the bubbles in F/M steel, and it is the deformation and mutual squeezing of bubbles under compression that causes the coalescence of tightly arranged bubbles. Furthermore, helium bubbles can act as dislocation sources to emit dislocations under compression, and the emitted dislocations can in turn envelope around the helium bubbles, thus hindering bubble coalescence and leading to the formation of deformed bubbles.

Prediction of acoustical behavior of granular material stacks as measured in a standing wave tube by using a Biot theory-based model

The acoustical behavior of granular materials, such as activated carbon and silica gel, has drawn attention in recent studies, due to their favorable properties such as good low frequency sound absorption. Like other more traditional porous materials, granular materials can also be tested in a standing wave tube for a convenient assessment of their acoustical properties. However, the behavior of granular materials stacked in a standing tube is more complex than that of traditional materials. For example, the response of lightweight glass bubbles reveals a clear dependence on the sound pressure level of the input signal. Also, when tested in standing wave tubes of different diameters, the same type of granular materials displays differences in their behavior. The apparent stiffness of granule pack is also related to the depth of the stack. In the present work, a model based on Biot theory is proposed, together with a consideration of the effect of the change of boundary conditions and the granule stack stiffness in different test configurations. The model is realized by using a finite difference method, and the simulation results are compared with measurements of different types of granular materials.

Non-linear response of colloid monolayers at high-frequency probed by ultrasound-driven microbubble dynamics.

High-frequency interfacial rheology of complex interfaces remains challenging yet it is central to the performance of multiphase soft matter products. We propose to use ultrasound-driven bubble dynamics to probe the high-frequency rheology of a colloid monolayer used as model system with controlled interactions and simultaneous monitoring of the microstructure. We hypothesize that by comparing the response of colloid-coated bubbles with that of a bare bubble under identical experimental conditions, it is possible to detect the non-linear response of the monolayer and use it to extract interfacial rheological properties at 104s-1. Using high-speed video-microscopy, the dynamics of colloid-coated bubbles were probed to study the micromechanical response of the monolayer to high-frequency deformation. Protocols analogous to stress-sweep and frequency-sweep were developed to examine the stress-strain relationships. A simple model, motivated by the observed non-linear responses, was developed to estimate the interfacial viscoelastic parameters. The estimated elastic moduli of colloid monolayers at 104s-1 are about an order of magnitude larger than those measured at 1 s-1. The monolayers exhibit non-linear viscoelasticity for strain amplitudes as small as 1%, and strain-softening behaviour. These findings highlight the applicability of acoustic bubbles as high-frequency interfacial probes.

Dynamic Response of Nanoscale He Bubbles in Single Crystal Al during Release from a High-Pressure State

Previous researches have presented some knowledge about the shock loading and unloading of the nanoscale He bubble. However, the He bubble will undergo a long high-pressure adiabatic relaxation process after being shocked. This work focuses on the release path of the nanoscale He bubble in single crystal Al from a stable high-pressure state by molecular dynamics method. Firstly, we consider the case that two opposite release waves meet at the center of the He bubble. Combined with the analysis of deformation mechanism and stress waveform around the He bubble, the difference of evolution law of He bubble under different pressure conditions is revealed. The evolution of the number and distribution of voids with or without the He bubble is compared. And the nucleation region gradually extends to both sides of the He bubble with the increase of initial Hugoniot pressure. Moreover, when a single unloading wave is considered to sweep through the He bubble, the microjet formation in the He bubble is found due to the pressure gradient effect. The shape and velocity distribution of internal and surface jets are discussed.

Quantitatively Monitoring Bubble-Flow at a Seep Site Offshore Oregon: Field Trials and Methodological Advances for Parallel Optical and Hydroacoustical Measurements

Two lander-based devices, the Bubble-Box and GasQuant-II, were used to investigate the spatial and temporal variability and total gas flow rates of a seep area offshore Oregon, United States. The Bubble-Box is a stereo camera–equipped lander that records bubbles inside a rising corridor with 80 Hz, allowing for automated image analyses of bubble size distributions and rising speeds. GasQuant is a hydroacoustic lander using a horizontally oriented multibeam swath to record the backscatter intensity of bubble streams passing the swath plain. The experimental set up at the Astoria Canyon site at a water depth of about 500 m aimed at calibrating the hydroacoustic GasQuant data with the visual Bubble-Box data for a spatial and temporal flow rate quantification of the site. For about 90 h in total, both systems were deployed simultaneously and pressure and temperature data were recorded using a CTD as well. Detailed image analyses show a Gaussian-like bubble size distribution of bubbles with a radius of 0.6–6 mm (mean 2.5 mm, std. dev. 0.25 mm); this is very similar to other measurements reported in the literature. Rising speeds ranged from 15 to 37 cm/s between 1- and 5-mm bubble sizes and are thus, in parts, slightly faster than reported elsewhere. Bubble sizes and calculated flow rates are rather constant over time at the two monitored bubble streams. Flow rates of these individual bubble streams are in the range of 544–1,278 mm3/s. One Bubble-Box data set was used to calibrate the acoustic backscatter response of the GasQuant data, enabling us to calculate a flow rate of the ensonified seep area (∼1,700 m2) that ranged from 4.98 to 8.33 L/min (5.38 × 106 to 9.01 × 106 CH4 mol/year). Such flow rates are common for seep areas of similar size, and as such, this location is classified as a normally active seep area. For deriving these acoustically based flow rates, the detailed data pre-processing considered echogram gridding methods of the swath data and bubble responses at the respective water depth. The described method uses the inverse gas flow quantification approach and gives an in-depth example of the benefits of using acoustic and optical methods in tandem.

A model for bubble dynamics in a protein solution

This paper presents a model for bubble dynamics in a protein solution, including varying surface tension and dynamic adsorption/desorption of protein onto the bubble surface. We model the protein-coated bubble surface as a linear viscoelastic interface. Two cases are studied to understand the importance of the surface excess stress: (1) bubble dissolution in a protein solution due to gas diffusion; and (2) bubble response to an imposed fluctuating pressure field. In the first case study, the surface excess stress stabilizes the bubble against dissolution. Initially, the surface excess stress is negligible, and the dissolution rate is governed by the Weber number, which compares the gas inertial force and the surface tension force. As the bubble shrinks, the surface excess stress grows and eventually balances the surface tension. After that, the dissolution rate is governed by the protein desorption rate and the elasto-capillary number, which compares the surface tension and the surface dilatational elasticity. Our model predictions for the dissolution process agree with experiments before the bubble buckles. In the second case study, the surface dilatational viscosity and dilatational elasticity add resistance and stiffness to the system, respectively. Including the surface excess stress increases (or reduces) the amplitude of the bubble radius if the frequency of the imposed fluctuating pressure is greater (or less) than a critical value. These results highlight the importance of the surface rheology on the protein-coated bubble dynamics, which has applications in drug delivery and ultrasound contrast agents.

Atomistic study on the dynamic response of helium bubbles to high-energy displacement cascades in tungsten

In a fusion reactor, plasma-facing materials simultaneously suffer high-flux low-energy helium/hydrogen irradiation and high-energy neutron bombardment. Numerous modeling studies have focused on radiation damage caused by individual particles, but ignored their synergistic effects. In this study, molecular dynamics simulations were performed to investigate the cascade damage near a pre-existing helium bubble in tungsten. The existence of helium bubbles generally inhibits defect generation but enhances interstitial-type dislocation loop formation. Furthermore, the distance between the primary knock-on atom and the bubble plays an important role in defect evolution. This corresponds to the defect distribution characteristics of the cascade damage in the perfect crystal. In addition, the change in morphology of helium bubbles during cascade damage was considered. Cascade-induced ballistic dissolution of helium from bubbles dominates helium ejection, but damage-assisted thermal dissolution is also observed. This work can contribute to understanding complex damage mechanisms in multiple irradiation fields, such as the fusion environment.

Study on the cell-collector-bubble interfacial interactions during microalgae harvesting using foam flotation

Foam flotation is an economical and efficient technology for microalgae harvesting. However, the mechanism of cell-collector-bubble interfacial interactions remains to be elucidated. There are two distinct hypotheses regarding the mechanism of microalgae foam flotation. In this study, the cationic surfactant N-cetyl-N-N-N-trimethylammonium bromide (CTAB), which acts as a partition between Chlorella sorokiniana cells and bubbles, is quantified and the zeta potential response of cells and bubbles after adsorption of CTAB is calculated to reveal the interfacial mechanism of the cells-collector-bubble interfacial interactions. The results indicated that more than 90% of CTAB was preferentially adsorbed on the bubbles, which reversed the surface charge of bubbles from negative (−20 mV) to positive (6.1 mV). However, only 0%–3% CTAB was observed on the microalgae cells, suggesting its limited influence on the negatively charged microalgae cells (from −22.3 to −18.6 mV). During microalgae foam flotation, the nonpolar tails of CTAB were first inserted into the bubble through hydrophobic interactions, leaving the positively charged polar heads outside; further, the CTAB-covered positively charged bubbles captured the negatively charged cells by electrostatic attraction. A feasible mechanism was proposed to understand the interfacial interaction of the microalgae cell-CTAB-bubble. By understanding the mechanism of foam flotation, efficient and cost-effective collectors and devices for microalgae harvesting using foam flotation can be developed.

Hemoglobin microbubbles for in vivo blood oxygen level dependent imaging: Boldly moving beyond MRI

Microbubbles are gas-filled, micron-sized particles stabilized by lipid, protein, or polymer shells. They scatter ultrasound energy efficiently due to their compressible gas cores, making them excellent blood pool contrast agents in ultrasound imaging. In this project, we have developed a novel oxygen-sensitive hemoglobin-shell microbubble designed to acoustically detect blood oxygen levels in vivo. We hypothesized that structural changes in the hemoglobin in response to varying oxygen levels will alter the mechanical properties of the bubble shell, resulting in detectable changes in the bubble acoustic signature. In this project, we have (1) optimized the hemoglobin bubble formulation for in vivo circulation, (2) demonstrated that the hemoglobin shell is still responsive to oxygen after formulation, and (3) characterized the acoustic response of the microbubbles at varying oxygen levels. Our preliminary results show a strong correlation between the oxygen concentration in the solution and the acoustic response of bubbles, suggesting that they would serve as excellent oxygen sensors. If successful, in vivo sensing of oxygen levels would have numerous benefits, including evaluating the hypoxic regions in tumors and in the brain, among other blood-oxygen-level-dependent (BOLD) imaging applications.

Cavitation and microbubble modeling

Bubbles in tissue may either help or hinder biomedical ultrasound. Exogenously introduced ultrasound contrast agents may comprise suspensions of micrometer-sized gas bubbles of sulfur hexafluoride, perfluorocarbon, or other low-solubility gas that are stabilized against dissolution by shells of lipids, proteins or synthetic, or alternatively, quasi-stable micro-droplets of certain liquids that nucleate gas bubbles in response to an impinging acoustic beam. However, tiny vapor bubbles may form spontaneously in tissues and act as potentially damaging cavitation nuclei under the influence of an acoustic wave. Microbubbles respond to the acoustic field by contracting and expanding to a much greater extent than does the surrounding tissue. This ‘acoustic cavitation’ may be violent, producing highly reactive chemical species, emission of ultraviolet and soft x-ray photons, and radiated shock waves, or less powerful, inducing, e.g., continuous heat production, radiation forces on neighboring particles, and microstreaming. Much early work assumed cavitation bubbles were surrounded by simple liquids, but biological tissues are viscoelastic, which can significantly affect bubble responses and thus must be considered. Mathematical models for these and related processes will be presented and compared, and details of their various physical mechanisms and the effects they may produce in biological tissue will be discussed.

On the Cover: Having Fun with Bubbles

Every time we celebrated Easter together, my friend would hide eggs filled with candy and special coins for the kids to have fun egg-hunting. After all the eggs had been found—sometimes with kind help from those who had done the hiding work—we would enjoy seeing the kids blow bubbles. They never tire of having fun with bubbles. It turns out psychometricians can have fun with bubbles too, although gaining insights is really the main purpose. Digital assessments allow for the development of Technology-Enhanced Items (TEIs) that create richer interactions with content, often resulting in response patterns beyond conventional multiple-choice items. Traditionally, test developers specify scoring rubrics that map response patterns into item scores (e.g., 1,2,3). Scoring rubrics are often self-evident for multiple-choice items and simple TEIs. However, for items eliciting large numbers of response patterns (some unanticipated), developing scoring rubrics based on expert judgment alone (absent data) can be challenging. Bubble plots are particularly helpful in informing scoring rubric development and/or item revision. In bubble plots, each distinct observed response pattern is represented by a bubble; in this example, there are 306 bubbles - one for each observed response pattern. Bubble size is proportional to the number of test-takers providing the given response pattern. Bubbles are aligned along the x-axis according to the average EAP score of test-takers represented by the bubble. Bubbles are placed on the y-axis according to the item score awarded to that specific response pattern, determined by the scoring rubric. Average ability estimates across all observed response patterns for each item score are on the y-axis in parentheses. For visual ease, all responses earning the same item score have the same color (e.g., all green bubble responses receive full credit). EAP is used as the ability estimate, but other estimates such as raw test score could be used as well. Bubble plots provide an intuitive way to connect psychometric properties of items with response patterns. For example, test takers with high ability tend to score higher on an item. But bubbles spanning a wide ability range at a given item score level might suggest an item has low power to differentiate among test takers at different ability levels. Such observations can sharpen focus on how specific responses are handled in scoring rubrics. Interested readers may contact Edward Kulick (ekulick@ets.org) for questions on this graphic. For bubble plots in general, I would recommend both authors and readers pay attention to the bubble size that can be determined by either the diameter or the area. For kids who have fun with bubbles, they do not care about the difference between the diameter and the area—the larger the bubble is, the better. But for scientific presentation, it is crucial for the authors and readers to be on the same scale because doubling the diameter of a bubble (shown as a disk) is equivalent to quadrupling its area!

Dynamics of an externally driven cavitation bubble in an elastic microconfinement.

The subject of the present study is the dynamics of a single cavitation bubble in a spherical liquid cell surrounded by an infinite elastic solid. It is shown that volume confinement strongly affects the manifestation of the classical cavitation Blake threshold. In particular, at liquid cell sizes smaller than some critical size, the cavitation is completely suppressed by volumetric confinement. The system of equations for the dynamics of a confined bubble, accounting for the mass of gas in the bubble, surface tension, liquid compressibility, solid elasticity, and damping due to viscosity in the liquid cell, is derived. The pressure in the solid far away from the bubble is used as an external driving force. Linear analysis of the bubble dynamics, including consideration of the natural frequency and amplitude-phase frequency response of the bubble-in-cell system, is conducted. In the nonlinear case, bifurcation diagrams are considered to determine the dynamic response of small and large bubbles in the states below and above the cavitation threshold, respectively.